Properties

Label 5635.148
Modulus $5635$
Conductor $115$
Order $44$
Real no
Primitive no
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5635, base_ring=CyclotomicField(44))
 
M = H._module
 
chi = DirichletCharacter(H, M([33,0,6]))
 
pari: [g,chi] = znchar(Mod(148,5635))
 

Basic properties

Modulus: \(5635\)
Conductor: \(115\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(44\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{115}(33,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 5635.cc

\(\chi_{5635}(148,\cdot)\) \(\chi_{5635}(442,\cdot)\) \(\chi_{5635}(638,\cdot)\) \(\chi_{5635}(687,\cdot)\) \(\chi_{5635}(1422,\cdot)\) \(\chi_{5635}(1667,\cdot)\) \(\chi_{5635}(2108,\cdot)\) \(\chi_{5635}(2353,\cdot)\) \(\chi_{5635}(2402,\cdot)\) \(\chi_{5635}(2843,\cdot)\) \(\chi_{5635}(2892,\cdot)\) \(\chi_{5635}(3333,\cdot)\) \(\chi_{5635}(3823,\cdot)\) \(\chi_{5635}(4068,\cdot)\) \(\chi_{5635}(4362,\cdot)\) \(\chi_{5635}(4607,\cdot)\) \(\chi_{5635}(4803,\cdot)\) \(\chi_{5635}(5048,\cdot)\) \(\chi_{5635}(5097,\cdot)\) \(\chi_{5635}(5587,\cdot)\)

sage: chi.galois_orbit()
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Related number fields

Field of values: \(\Q(\zeta_{44})\)
Fixed field: \(\Q(\zeta_{115})^+\)

Values on generators

\((3382,346,2696)\) → \((-i,1,e\left(\frac{3}{22}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(8\)\(9\)\(11\)\(12\)\(13\)\(16\)
\( \chi_{ 5635 }(148, a) \) \(1\)\(1\)\(e\left(\frac{1}{44}\right)\)\(e\left(\frac{19}{44}\right)\)\(e\left(\frac{1}{22}\right)\)\(e\left(\frac{5}{11}\right)\)\(e\left(\frac{3}{44}\right)\)\(e\left(\frac{19}{22}\right)\)\(e\left(\frac{5}{22}\right)\)\(e\left(\frac{21}{44}\right)\)\(e\left(\frac{7}{44}\right)\)\(e\left(\frac{1}{11}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 5635 }(148,a) \;\) at \(\;a = \) e.g. 2